Theorems · Theorem · group theory
AddCommute.zsmul_add
∀ {G : Type u_1} [inst : SubtractionMonoid G] {a b : G}, AddCommute a b → ∀ (n : ℤ), n • (a + b) = n • a + n • b- Defined in
- Mathlib.Algebra.Group.Commute.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
- Assumes
- SubtractionMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- neg_add_revproof · cited by 236
- SubtractionMonoidstatement and proof · cited by 208
- AddCommutestatement and proof · cited by 185
- natCast_zsmulproof · cited by 118
- negSucc_zsmulproof · cited by 45
- AddCommute.eqproof · cited by 18
- AddCommute.nsmul_nsmulproof · cited by 4
- AddCommute.add_nsmulproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Even.zsmul_rightproof · cited by 0